Equivalences of monoidal model categories

Stefan Schwede, Brooke Shipley

Abstract.
We construct Quillen equivalences between the model categories of
monoids (rings), modules and algebras over two Quillen equivalent
model categories under certain conditions. This is a continuation of
our earlier work where we established model categories of monoids,
modules and algebras [Algebras and modules in monoidal model
categories, Proc. London Math. Soc. 80 (2000), 491-511]. As an
application we extend the Dold-Kan equivalence to show that the model
categories of simplicial rings, modules and algebras are Quillen
equivalent to the associated model categories of connected
differential graded rings, modules and algebras. We also show that our
classification results from [Stable model categories are categories of
modules, Topology, 42 (2003) 103-153] concerning stable model
categories translate to any one of the known symmetric monoidal model
categories of spectra.